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| ====== FSc Part 1 (KPK Boards) ====== | ====== FSc Part 1 (KPK Boards) ====== | ||
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| Notes of FSc Part 1 of "A Textbook of Mathematics For Class XI" published by Khyber Pakhtunkhwa Textbook Board, Peshawar. We are posting the notes chapter-wise. These notes are shared as open educational resources. This page will be continuously updated. | Notes of FSc Part 1 of "A Textbook of Mathematics For Class XI" published by Khyber Pakhtunkhwa Textbook Board, Peshawar. We are posting the notes chapter-wise. These notes are shared as open educational resources. This page will be continuously updated. | ||
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| === Download === | === Download === | ||
| - | <callout type=" | + | <callout type=" |
| - | **{{: | + | |
| - | </ | + | |
| - | ===== Chapter 02: Matrices and Determinants ===== | + | ===== Chapter 02: Matrices and Determinants ===== |
| === Objectives === | === Objectives === | ||
| After reading this unit the students will be able to: | After reading this unit the students will be able to: | ||
| + | |||
| * know a matrix and its notations, order of a matrix and equality of two matrices. | * know a matrix and its notations, order of a matrix and equality of two matrices. | ||
| * understand types of matrices, algebra of matrices and some properties of matrix addition and scalar multiplication. | * understand types of matrices, algebra of matrices and some properties of matrix addition and scalar multiplication. | ||
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| * know elementary row and column operations on matrices. | * know elementary row and column operations on matrices. | ||
| * recognize echelon and reduced echelon form of a matrix and rank of a matrix. | * recognize echelon and reduced echelon form of a matrix and rank of a matrix. | ||
| - | * solve a system of linear equations of both homogeneous and non-homogeneous equations... | + | * solve a system of linear equations of both homogeneous and non-homogeneous equations. |
| === Download === | === Download === | ||
| + | |||
| <callout type=" | <callout type=" | ||
| | | ||
| + | </ | ||
| + | |||
| + | ===== Chapter 03: Vectors ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to: | ||
| + | * differentiate between scalar and vector quantities. | ||
| + | * give geometrical representation of a vector in a space. | ||
| + | * know the fundamental defintion of vector using geometrical as well as analytical representation. | ||
| + | * use vector to prove simple theorems of descriptive geometry. | ||
| + | * recognize rectangular coordinate system in space. | ||
| + | * define unit vectors i, j and k. | ||
| + | * repeat all fundamental definitions of vector in plane for space. | ||
| + | * know properties of vector addition and cross or vector product. | ||
| + | * define scalar triple product of vectors. | ||
| + | * express scalar triple product of vectors in terms of components (determinantal form). | ||
| + | * | ||
| + | === Download === | ||
| + | |||
| + | <callout type=" | ||
| + | | ||
| + | </ | ||
| + | |||
| + | ===== Chapter 4: Sequences ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to: | ||
| + | |||
| + | * define a sequence and its terms. | ||
| + | * recognize triangle, factorial and Pascal sequence. | ||
| + | * know the definition of an arithmetic sequence. | ||
| + | * define arithmetic mean and arithmetic series. | ||
| + | * solve real life problems involving arithmetic series. | ||
| + | * define a geometric sequence. | ||
| + | * solve problems involving geometric sequences. | ||
| + | * define geometric mean and geometric series. | ||
| + | * solve real life problems involving geometric series. | ||
| + | * recognize a harmonic sequence and find its nth term. | ||
| + | * define harmonic mean and insert n harmonic means between two numbers. | ||
| + | |||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| + | </ | ||
| + | |||
| + | ===== Chapter 5: Miscellaneous Series ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to: | ||
| + | |||
| + | * know sigma $(\sum)$ sign and evaluation of $\sum n$, $\sum n^2$ and $\sum n^3$. | ||
| + | * understand arithmetical-geometric series and its sum of $n$ terms. | ||
| + | * know method of differences and its uses. | ||
| + | * use the partial fraction to find the sum to $n$ terms and to infinity of the series of the type $$\frac{a}{a(a+d)}+\frac{a}{(a+d)(a+2d)}+...$$ | ||
| + | |||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| + | </ | ||
| + | ===== Chapter 6: Permutation, | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to: | ||
| + | |||
| + | * know Kramp' | ||
| + | * recognize the fundamental principle of counting and its illustration by using tree diagram. | ||
| + | * understand the concept of permutation and know the notation $^nP_r$. | ||
| + | * Prove the formula ^nP_r=n(n-1)(n-2)...(n-r+1), | ||
| + | * define combination and know the notation $^nC_r=\left(\begin{smallmatrix}n\\ r\end{smallmatrix} \right)=\frac{n!}{r!(n-r)!}$, | ||
| + | * define kind of events. | ||
| + | * recognize the formula $P(E)=\frac{n(E)}{n(S)}$, | ||
| + | * recognize the addition theorem (or law) of probability and its deduction. | ||
| + | * recognize the multiplication theorem (or law) of probability and its deduction. | ||
| + | * Use theorem of addition and multiplication of probability to solve related problems. | ||
| + | |||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| + | </ | ||
| + | ===== Chapter 7: Mathematical Induction and Binomial Theorem ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to: | ||
| + | |||
| + | * know the principle of mathematical induction. | ||
| + | * apply the principle to prove the statements, identities or formulae. | ||
| + | * state and prove binomial theorem for positive integral index. | ||
| + | * expand $(x+y)^n$ using binomial theorem and find its general form. | ||
| + | * understand pascal' | ||
| + | * know binomial series and its use to find the sum of the given series. | ||
| + | |||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| + | </ | ||
| + | |||
| + | ===== Chapter 8: Functions and Graphs ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to | ||
| + | |||
| + | * know linear, quadratic and square root functions. | ||
| + | * define inverse functions and find their domain and range. | ||
| + | * sketch the graph of the function $y=x^n$ for different values of $x$. | ||
| + | * sketch the graph of quadratic function. | ||
| + | * predict function from their graph. | ||
| + | * find the intersecting point of intersecting graphs of a linear functions and coordinate axes, two linear functions and a linear and quadratic function. | ||
| + | * solve graphically appropriate problems from daily life. | ||
| + | |||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| + | </ | ||
| + | |||
| + | ===== Chapter 9: Linear Programming ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to | ||
| + | |||
| + | * define linear programming (LP) as planning of allocation of limited resources to obtain optimal result. | ||
| + | * understand linear inequalities in one and two variables and its importance in real life problems. | ||
| + | * know the feasible region and identification of feasible region of simple LP problems. | ||
| + | * define optimal solution of an LP problem. | ||
| + | * find optimal solution graphically of LP problems. | ||
| + | * solve real life simple LP problems. | ||
| + | |||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| + | </ | ||
| + | |||
| + | ===== Chapter 10: Trigonometric Identities of Sum and Difference of Angles ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to | ||
| + | |||
| + | * know the fundamental law of trigonometry and deduction of trigonometric identities from it. | ||
| + | * understand trigonometric ratios and allied angles. | ||
| + | * use fundamental law and its deduction to derive trigonometric ratios of allied angles. | ||
| + | * derive double, half and triple angle identities from fundamental law and its deduction. | ||
| + | * express the product of sines and cosines as sum or differences of sines and cosines. | ||
| + | * express the sums or differences of sines and cosines as product. | ||
| + | |||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| + | </ | ||
| + | |||
| + | ===== Chapter 11: Application of Trigonometry ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to | ||
| + | * find the solution of right angles triangle. | ||
| + | * understand oblique triangles and find solution of such triangles, using the law of sines, cosines and tangents. | ||
| + | * derive the formula for finding the areas of triangles. | ||
| + | * know circum-circle, | ||
| + | * derive the formula for finding circum-radius, | ||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| + | </ | ||
| + | |||
| + | ===== Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations ===== | ||
| + | === Objectives === | ||
| + | After reading this unit the students will be able to | ||
| + | * know trigonometric functions and their domain and range. | ||
| + | * define periodic, even/odd and translation properties of the graph of $\sin \theta$, $\cos \theta$ and $\tan \theta$. | ||
| + | * solve trigonometric equations of the type $\sin\theta=k$, | ||
| + | * solve graphically the trigonometric equations of the type $\sin\theta=\frac{\theta}{2}$, | ||
| + | * define inverse trigonometric functions and their domain and range. | ||
| + | * prove the addition and subtraction formulae of inverse trigonometric functions and know their applications. | ||
| + | * solve general trigonometric equations. | ||
| + | |||
| + | ===Download=== | ||
| + | <callout type=" | ||
| + | **{{: | ||
| </ | </ | ||
| {{tag> FSc KPK_FSc_Part1}} | {{tag> FSc KPK_FSc_Part1}} | ||